Interferometer with continuously varying path length measured in wavelengths to the reference mirror

ABSTRACT

An interferometer in which the path length of the reference beam, measured in wavelengths, is continuously changing in sinusoidal fashion and the interference signal created by combining the measurement beam and the reference beam is processed in real time to obtain the physical distance along the measurement beam between the measured surface and a spatial reference frame such as the beam splitter. The processing involves analyzing the Fourier series of the intensity signal at one or more optical detectors in real time and using the time-domain multi-frequency harmonic signals to extract the phase information independently at each pixel position of one or more optical detectors and converting the phase information to distance information.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit of the priority of U.S. ProvisionalPatent Application No. 61/620,658 filed Apr. 5, 2012 entitledINTERFEROMETER WITH CONTINUOUSLY VARYING NUMBER OF WAVELENGTHS TO THEREFERENCE MIRROR.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under Order No.NNX09CD59P awarded by NASA on Jan. 22, 2009, and under Award No.IIP-1013289 awarded by NSF on May 11, 2010. The government has certainrights in the invention.

TECHNICAL FIELD

The present application relates to the field of measuring the topology,or surface profile, of a surface, specifically performing highresolution, non-contact measurements, with high signal-to-noise-ratio(SNR), via interferometry.

BACKGROUND

Interferometry is widely used to measure changes in distance and tomeasure the topology of a surface at the micro level. The latterapplication is often referred to as surface profiling. The generalprinciple, illustrated with reference to a conventional interferometrysystem 100 (see FIG. 1), involves splitting a beam 11 of light into twoportions 12 and 15, reflecting one portion 12 of the beam 11 from areference surface 13 and the other portion 15 from a measured surface16, combining the two portions 12, 15 of the beam 11 into a single beam18, and detecting the combined, single beam 18 via an optical detector17. Beams of light illustrated in this and the other drawing figuresherein are shown as double lines, signifying the outside opposing edgesof the diameter of the beam. The beam that starts from the light source10 and is reflected from the reference surface 13 and passes to theoptical detector 17 is the reference beam, and the beam that starts fromthe light source 10, is reflected from the measured surface 16 andpasses to the optical detector 17 is the measurement beam.

When the optical path length of the reference beam is equal to theoptical path length of the measurement beam, then the two beamsinterfere constructively. If single wavelength light is used and thepaths along which the measurement beam and the reference beam traveldiffer by half a wavelength, then the two beams of light interferedestructively, and the optical detector 17 detects a signal of minimumamplitude. Similarly, whenever the difference between the two paths isn*(λ/2), where n is an odd integer and λrepresents the wavelength of thelight, the optical detector 17 again detects a signal of minimum level,and when the difference between the two paths is m*(λ/2), where m is aneven integer, the optical detector 17 detects a maximum signal. If theobject being measured (e.g., the measured surface 16) moves half awavelength toward or away from the beam splitter 21, the path length ofthe measurement beam will change by one complete wavelength, and theoptical detector 17 will go through one complete cycle of intensitydetected by the optical detector 17. A region in which the combinedintensity of the reference beam and the measurement beam is at a minimumis referred to as a fringe. Quarter wave plates 22 and 23, shown in FIG.1, may be optionally inserted in the reference beam path and themeasurement beam paths, respectively, to reduce errors caused byreflections, as is known in the art.

When a single optical detector is used to detect the average intensityof beam 18, the optical detector measures the difference in path lengthbetween the measurement beam and the reference beam. This configurationis useful to detect changes in distance between the measured surface 16and the beam splitter 21. If an optical detector with a two dimensionalarray of optical detecting elements, such as a CCD camera, is used, andthe diameter of the light beam is configured to be large enough toilluminate the complete two-dimensional optical detector, then eachelement of the optical detector acts as a separate optical detector, andthe system functions as multiple interferometers operating in parallel.The area of each optical detector element creates a pixel, a word whichis a contraction of the words “picture” and “element”. When the measuredsurface is not perfectly smooth, there will be different optical pathlengths for different pixels, causing phase differences between thesignals at different optical detector elements and therefore differentintensity signals at each detector element. The difference in intensityat different optical detector elements can be converted to phasedifferences, and the phase differences can be converted to distances,yielding a three-dimensional map of the topology of the area seen by thecomplete two-dimensional optical detector.

While multiple phase calculation methods exist, in general, a completemeasurement requires moving the reference surface in multiple discreteincrements to capture fringe pattern images at each position of thereference mirror while the measured surface does not move. Once theseimages are captured the data of the multiple frames are used tocalculate the phase information at the corresponding pixels. Thissurface profiling technique, in which the reference surface moves inmultiple discrete steps, is referred to as Phase Shifting Interferometryand equipment using this technique is referred to as a Phase ShiftingInterferometer (PSI).

Phase Shifting Interferometers cannot determine a step height withcertainty if the height changes instantaneously between neighboringpixels by more than plus or minus λ/2, because a PSI using singlewavelength light cannot distinguish between a phase change of ΔΦ and aphase change of ΔΦ+nλ, where ΔΦ is the phase difference between thereference beam and the measurement beam and n is an integer. Following asimilar principle, in order to measure a surface whose height ischanging relatively rapidly from one pixel to another, single wavelengthPSIs increment the movement of the reference surface (or the measuredsurface) by an amount which is less than λ/2 and assume that n, in theexpression ΔΦ+nλ/2, is zero. Moving the reference surface through afixed distance in small discrete increments and collecting intensitysignal information at each position of the reference surface requiresconsiderably more measurement time than acquiring intensity data at asingle position of the reference surface.

While interferometers using multiple wavelengths of light, or even whitelight, are better at measuring step height than single wavelength PSIs,such interferometers require moving the reference surface in discreteincrements over a distance far greater than λ/2, where λ is thewavelength used for a single wavelength interferometer, requiringadditional measurement time.

The lateral resolution of such a surface profiler is a function of boththe size of the elements in the optical detector and of the optics whichimage the measured surface onto the optical detector elements. In orderto obtain better lateral resolution, one uses greater magnification,resulting in a measurement of a smaller area of the measured surface.The software of typical Phase Shifting Interferometer systems can stitchtogether multiple images, taken by measuring one site, moving themeasured surface to another site, measuring at that site, etc., buttaking multiple images requires even more time. Further, the assumptionbehind stitching is that there is no system drift between adjacentimages, producing no discontinuities. Thermal drift and vibration cancreate errors in the stitched images. Errors caused by stitching and thelarge amount of time required to make measurements of suitable lateraland vertical resolution often make PSIs unsuitable for quality controlin a production environment.

Phase Shifting Interferometer measurements often suffer from errorsources such as inaccurate knowledge of the exact position of thereference mirror and inaccurate positioning of the intended discretepositions of the reference mirror. Further PSI interferometers cannotdistinguish between vibration of the measured surface, such as might becaused by sound waves impinging on the measured surface, from changes inthe actual roughness of the measured surface.

It would therefore be desirable to have interferometry systems andmethods that avoid at least some of the drawbacks of the conventionalinterferometry systems and methods described above.

SUMMARY

In accordance with the present application, interferometry systems andmethods are disclosed in which the path length of a reference lightbeam, measured in wavelengths, is continuously changing in sinusoidalfashion, and the interference signal created by combining a measurementlight beam and the reference light beam is processed in real time toobtain the physical distance along the measurement light beam between ameasured surface and a spatial reference frame such as a beam splitter.The processing involves analyzing the Fourier series of the intensitysignals at one or more optical detectors in real time, using thetime-domain multi-frequency harmonic signals to extract the phaseinformation independently at each pixel position of one or more opticaldetectors, and converting the phase information to distance information.

In accordance with a first aspect, the path length of the reference beamchanges in a sinusoidal oscillatory fashion. A beam splitter splits alight beam generated by a light source into a first portion and a secondportion. Further, a reference surface is disposed substantiallyperpendicular to the first portion of the beam, and a measured surfaceis disposed substantially perpendicular to the second portion of thebeam. The reference surface moves toward the beam splitter and then awayfrom the beam splitter, while maintaining substantial perpendicularityto the first portion of the beam, in a continuous oscillatory mannerthat is sinusoidal. The frequency of oscillation of the referencesurface is generally lower than the rate at which the optical detectorcollects data, allowing multiple sets of data per period of oscillationof the reference surface.

The waveform of the intensity at the optical detector isI=A+B cos(Δφ*sin(ω_(r) t)+φ),where A is a DC signal offset, ω_(r) is the angular frequency of themotion of the reference surface, B is the intensity amplitude of thewaveform, φ is the fringe phase (height information), and Δφ representsthe amplitude of the reference mirror modulation or oscillation.

The phase difference information is recovered by real-time analysis ofthis waveform, enabling a surface profile measuring system in which thetest object does not need to be stationary during the measurement. Forexample, the measured surface can move in the X direction, via themotion of a stage holding the sample or any other suitable mechanism andusing one or more position encoders or any other suitable mechanism todetermine the precise position of the moving sample, while the systemmeasures in the Y direction. In accordance with this first aspect, thesystem can detect the phase synchronously, providing surface profiledata with high signal-to-noise-ratio (SNR) since noise of frequenciesthat are not multiples of ω_(r) will be filtered out.

In accordance with a second aspect, the optical detector is atwo-dimensional array of optical detector elements and the output fromthe optical detector is two-dimensional intensity data. In accordancewith an exemplary aspect, if it is necessary to measure a surface whichis larger than the area of the second portion of the beam, then afteracquiring one image, the measured surface is displaced in X or Y, thesystem waits to allow vibration caused by the motion to settle, a newimage is acquired, and the system software stitches together the images.The same concept can be extended to acquire additional images, afteradditional movement of the measured surface in either the X or Y axis,or a combination of both.

In accordance with a third aspect, the optical detector is at least alinear array of optical detector elements and produces one dimensionalintensity data, for instance in the Y direction. In accordance with anexemplary aspect, the measured sample moves in the X direction whileintensity data in the Y direction are acquired. The effective imagecreated by moving the measured sample can be much larger than thatavailable by using an optical detector that supplies intensity data intwo dimensions. If it is necessary to measure larger surfaces, then itis possible to move the measured surface in the Y direction, wait forsettling, and then acquire new data while moving the measured surface inthe X direction. Similarly, the measured sample could move in the Ydirection, and the linear array of optical detector elements could bemounted to take data in the X direction.

In accordance with a fourth aspect, which is useful when measuring roundflat objects, such as the surface of magnetic hard disks, the onedimensional array of optical detector elements and/or the measuredsurface can be configured to move relative to one another to allow theone dimensional optical detector to perform a measurement along a radiusof the measured surface. In accordance with an exemplary aspect, the onedimensional array of optical detector elements measures along such aradius and the measured surface is rotated about its center as pixeldata are collected. If the length of the one dimensional opticaldetector is less than the radius needed to be measured, then multipleimages can be acquired by moving the linear array of optical detectorelements in the appropriate direction along the radius and acquiringdata during another rotation of the measured surface. To minimizemeasurement time, while maintaining a constant effective pixel size, thespeed of rotation of the measured surface may be increased as thedistance of the linear array of optical detector elements from thecenter of rotation decreases.

In accordance with the third and fourth aspects described above, thesample moves in one direction, while a linear array of optical detectorelements positioned in a substantially perpendicular direction collectsintensity data. The image captured during one complete movement of thesample can be increased by increasing the length of the linear array ofoptical detector elements. This can be achieved by various mechanisms ortechniques, including increasing the physical length of the array ofoptical detector elements or by using multiple interferometers,including multiple linear arrays of optical detectors, operating inparallel and positioned to extend the equivalent length of a singlearray.

The interferometry system according to the first aspect described aboveis useful for distance measurement, where the measured surface moves.The method of phase detection via analyzing the complex waveformproduced by the oscillating reference mirror and the moving measuredsurface can be implemented at lower cost than conventional methods, andthe performance requirement of the analog to digital converter used todigitize the intensity signal can be lower than required by conventionalmethods.

In accordance with the second, third, and fourth aspects describedabove, it is desirable to process intensity data from all the opticaldetector elements in parallel, in order to create real time, time-domaindata. This can be achieved via pipe-lining, in which the same hardwarequickly processes data from one optical detector element and thenprocesses data from the next optical detector element at the followingprocessor clock cycle, producing fully processed data at a rate that canbe as fast as the rate that data are captured by the entire group ofoptical detector elements. If lower spatial frequency of the image isallowable, then the rate of data capture can be even faster.

In accordance with a fifth aspect, a data processing approach, referredto herein as “active mixing”, allows producing fully processed opticaldetector intensity data at a rate equal to the rate that intensity dataare captured by the optical detector. In accordance with a sixth aspect,another data processing approach, which is referred to herein as“pseudo-active mixing”, allows producing fully processed data at onequarter the rate at which data are captured by the optical detector,without the need for modulating the light intensity, thus withoutincorporating an electro-optic component that can increase cost.

In accordance with a sixth aspect, an interferometry system includes abeam splitter operative to split a source light beam into a referencebeam and a first measurement beam. The reference beam and the firstmeasurement beam each have an associated path, and an associated pathlength measured in wavelengths. A measured sample is disposed in thepath of the first measurement beam. The interferometry system furtherincludes a first component operative to vary the path length of thereference beam in a sinusoidal fashion. In addition, the interferometrysystem includes at least one second component operative to detect atleast one second measurement beam that is based upon the reference beamand the first measurement beam, to generate at least one opticaldetector signal corresponding to the second measurement beam, and toanalyze Fourier series components of the optical detector signal in thetime-domain to determine a phase shift in the reference beam or thefirst measurement beam caused by the measured sample, a change in thepath length of the reference beam or the first measurement beam, and/ora distance between the beam splitter and the measured sample.

The presently disclosed interferometry systems and methods can acquiresurface topology data of a large measured surface at a rate which isfaster than conventional systems and methods. Further, the disclosedsystems and methods can provide fast surface profile measurements withimproved vertical resolution and measurement accuracy. Moreover, thedisclosed systems and methods have the ability to capture a highresolution single measurement image of an area that is larger thanpreviously possible using conventional systems and methods. Thedisclosed systems and methods can also acquire data in real time inorder to allow time-domain digital filtering techniques. In addition,the disclosed systems and methods allow simultaneous measurement of aknown measured surface, and an unknown measured surface, in order tocorrect for systematic measurement errors.

Other features, functions, and aspects of the invention will be evidentfrom the Drawings and/or the Detailed Description of the Invention thatfollow.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be more fully understood with reference to thefollowing Detailed Description of the Invention in conjunction with thedrawings of which:

FIG. 1 is a schematic diagram showing a conventional Michelsoninterferometer;

FIG. 2 is a schematic diagram showing an interferometry systemconfigured for surface profiling, in accordance with an exemplaryembodiment of the present application;

FIG. 3 is a schematic diagram showing an interferometry system withquarter wave plates and a moveable reference surface, in accordance withanother exemplary embodiment of the present application;

FIGS. 4a and 4b are diagrams showing the motions of a measured part withreference to a linear array of optical detector elements, in accordancewith further exemplary embodiments of the present application;

FIG. 5 is a diagram showing the measurement of a surface with highspatial frequency in one axis;

FIG. 6 is a block diagram showing a data path;

FIG. 7 is a schematic diagram showing a method of correcting systematicerrors in collected data, in accordance with still another exemplaryembodiment of the present application;

FIGS. 8a and 8b are block diagrams illustrating overviews of the dataprocessing done by a signal processing component;

FIG. 9 is a schematic diagram showing an illustrative example ofpipe-lining;

FIG. 10 is a series of plots showing the signals in an active mixingsignal processing technique;

FIG. 11 is a series of plots showing the signals in a pseudo-activemixing signal processing technique; and

FIG. 12 is a block diagram illustrating an overview of further dataprocessing done by a signal processing component.

DETAILED DESCRIPTION

The disclosure of U.S. Provisional Patent Application No. 61/620,658filed Apr. 5, 2012 entitled INTERFEROMETER WITH CONTINUOUSLY VARYINGNUMBER OF WAVELENGTHS TO THE REFERENCE MIRROR is incorporated herein byreference in its entirety.

FIG. 2 shows an interferometry system 200, such as a Michelsoninterferometer, functioning as the optical sensing apparatus for surfaceprofiling. It includes of a monochromatic light source 212, a beamexpander 214, a beam splitter 218 with partially mirrored surface 216, areference mirror 202 with reference surface 204, a measured surface 210,an objective lens 220, and an optical detector 222.

The monochromatic light source 212 emits a light beam 226. The diameterof the beam 226 is enlarged via the beam expander 214 to produce a lightbeam 228 whose diameter is large enough to illuminate the desired imagearea of the measured surface 210. For example, the diameter of the beam226 might be 2-3 mm, and the beam expander 214 might be a 10× beamexpander, to produce the beam 228 whose diameter is 20-30 mm. The beam228 is split into two portions of approximately equal intensity 224 aand 230 a, for example via the beam splitter 218 whose internal mirroredsurface 216 is approximately 50% reflective to the wavelength of lightemitted from the light source 212 at an angle of incidence of 45degrees. Such beam splitters are commonly available. For example, themodel CM1-BS1 beam splitter, manufactured by Thorlabs, or any othersuitable beam splitter, may be employed. It is noted that a parallelplate mirror can be used instead of a beam splitter cube.

The beam 224 a reflects from the reference surface 204 and creates alight beam 224 b. Similarly the beam 230 a reflects from the measuredsurface 210 and creates a light beam 230 b. The reflected beam 224 benters the beam splitter 218, and approximately 50% of the beam travelsthrough the partially mirrored surface 216 toward the optical detector222. Similarly the reflected beam 230 b travels toward the beam splitter218 and is reflected from the partially mirrored surface 216 toward theoptical detector 222. Thus, the light beam 232 is a combination of thebeam 224 b reflected from the reference surface 204 and the beam 230 breflected from the measured surface 210.

The reference surface 204 is the surface of the reference mirror 202.The reference mirror 202 is positioned with the reference surface 204substantially perpendicular to the beams 224 a, 224 b. The referencesurface 204 is substantially flat, and portions of the beam 224 breflected from one area within the reference surface 204 experiencesubstantially the same optical path length as portions of the beam 224 breflected from other areas within the reference surface 204. Referencemirrors with flat surfaces are commonly available in different flatnessspecifications. Deviations from an ideal, perfectly flat, referencemirror create systematic errors in the measurement. These errors can besubtracted from the measurement of the measured surface, by storing theerror at each optical detector element, determined when measuring aknown, flat surface.

The beam 232 passes through the objective lens 220 and onto the opticaldetector 222. The optical detector 222 can be a single point detector, alinear array of optical detector elements, a two-dimensional array ofoptical detector elements, or any other suitable optical detector. Inthe case of either a linear array of optical detector elements, oftenreferred to as a “linear detector”, or a two-dimensional array ofoptical detector elements, each element creates one pixel ofinformation. The physical size of each element, reduced by themagnification of the objective lens determines the measurement area ofeach pixel. For example, an optical detector element whose physical sizeis a square area 10 microns on a side and a 5× objective lens allowsmeasuring 2 micron pixels of the measured surface.

FIG. 3 shows an interferometry system 300, in which the optical pathlength of the beams 224 a, 224 b can change in an oscillatory fashionwhen the reference surface 204 moves toward the beam splitter 218 andaway from the beam splitter 218, while maintaining substantialperpendicularity to the beams 224 a, 224 b. A motion of the referencesurface 204 of length x in the direction towards the beam splitter 218causes the optical path length to decrease by 2×. Similarly, a motion ofthe reference surface 204 of x away from the beam splitter 218 causesthe optical path length to increase by 2×. FIG. 3 illustrates anexemplary method of achieving this motion. In FIG. 3 the referencemirror 202 is attached to a substantially fixed, high mass object 342via three piezoelectric transducers (PZTs) 340 a, 340 b, and 340 c. PZTs340 a, 340 b, and 340 c are controlled by three high voltage amplifiers(not shown), and when the voltage across each PZT increases, the PZTchanges length, moving the reference mirror 202 in a direction toward oraway from the beam splitter 218, while maintaining perpendicularity tothe beams 224 a, 224 b. When the voltage across a PZT returns to itsoriginal value, the length of the PZT returns to its original value.High voltage of the opposite polarity creates a change in the PZT lengthin the opposite direction. The three PZTs 340 a, 340 b, and 340 c andtheir associated high voltage amplifiers are matched so as to maintainsubstantial perpendicularity to the beams 224 a, 224 b as the PZTs 340a, 340 b, and 340 c move the reference surface 204 toward the beamsplitter 218 and away from it. The object 342 has very high inertialmass compared to the reference mirror 202, and as the PZTs 340 a, 340 b,and 340 c move the reference mirror 202, substantially all of the motionis movement of the reference mirror 202 containing the reference surface204, with substantially no motion of the fixed object 342. The thicknessof the reference mirror 202, the material of the reference mirror 202,and the placement of the PZTs 340 a, 340 b, and 340 c are chosen toavoid dynamic changes in flatness of the reference surface 204 as itmoves toward the beam splitter 218 and away from it in response toexcitation from the PZTs 340 a, 340 b, and 340 c. Putting a beamexpander (not shown) in the path of the beams 224 a, 224 b causes thebeam diameter hitting the reference surface 204 to be smaller than thebeam diameter of the beams 224 a, 224 b, allowing the reference mirror202 to be smaller and have lower mass. Thus it is possible to move thereference mirror 202 back and forth more rapidly without requiring morepowerful PZTs and without incurring significant dynamic distortion ofthe reference surface 204.

It is noted that any other suitable mechanisms of mounting the referencesurface 204 and moving it in an oscillatory motion may be employed, suchas using a single PZT and a flexure mount. As an example, the movementof the reference mirror 202 via a PZT can be accomplished by the modelP-720 PZT, manufactured by Physik Instrumente, GmbH. Moreover, while theexamples shown in FIGS. 3, 4 and 6 use a Michelson interferometerconfiguration, any other suitable interferometer configuration,including Mirau, Fizeau, Fabry-Perot, Twyman-Green, and Mach Zehnder,could also be used.

An alternative to moving the reference mirror 202 with the referencesurface 204 is modulating the wavelength of the light source 212. In anyof the illustrative embodiments disclosed herein, the oscillation of thewavelength of light can be substituted for the oscillatory motion of thereference mirror. Many techniques exist to modulate the wavelength of acoherent light source. One economical technique is to modulate thecurrent of a laser diode, such as Sanyo DL6147, to produce wavelengthmodulation. If the path length of the reference beam differs by ΔL fromthe path length of the measurement beam, then a wavelength shift of Δλof the light source 212 causes a phase shift of the interference fringeof 2πΔLΔλ/λ². Signal processing can correct for the consequential effectof changes in light amplitude caused by modulating the laser diodecurrent in order to modulate the wavelength.

An interferometry system in which the wavelength of the light beam 228is modulated instead of moving the reference mirror 202 is describedbelow with regard to FIG. 3. In such an interferometry system, becausethe reference mirror 202 is not moved, the PZTs 340 a, 340 b, and 340 c,as well as the high mass object 342, may be omitted. Further, one ofordinary skill in the art will appreciate that the wavelength of thelight beam 228 can be modulated by placing an optical component such asan acousto-optic modulator in the path of the light beam 226 emitted bythe light source 212 or in the path of the light beam 228 produced bythe beam expander 214, or by any other suitable technique.

Modulating the wavelength of the light beam 228 in sinusoidal fashiontypically allows a higher modulation frequency than moving the referencemirror 202 and produces a system with no moving parts. Further,modulating the wavelength of the light beam 228 obviates the need forthe high mass, substantially fixed object 342, reducing the mass of thetotal system. When using a laser diode as a light source, the change inintensity caused by modulating the diode current can be predicted ormeasured by a photo detector located near the laser diode, and thesignal processing apparatus can correct for the change in lightintensity of the laser diode.

In a first illustrative embodiment of the present application, a singlepoint optical detector is used, the reference mirror moves continuouslyin sinusoidal motion, and the signal processing apparatus determinesphase information by analyzing the output of the optical detector. Suchan interferometer is useful for measuring changes in distance.

In a second illustrative embodiment of the present application, atwo-dimensional optical detector is used, the reference mirror movescontinuously back and forth in sinusoidal motion, or the wavelength ofthe light source changes in sinusoidal fashion, and the signalprocessing apparatus determines phase information by analyzing theoutput of each element of the optical detector. Phase information isconverted to distance information by knowing the wavelength of lightproduced by light source 212. The image captured by the two-dimensionaloptical detector is equal to the physical size of the two-dimensionaloptical detector, reduced by the magnification of objective lens 220. Tomeasure surfaces larger than one image size, it is necessary to move themeasured surface in the X or Y direction, as appropriate, to apreviously unmeasured area, wait for the stage motion and any associatedvibration to settle, and capture an additional image. The process ofmoving to a new position, waiting for motion transients to settle, andthen repeating the previous acquisition process is referred to as a“Step and Repeat” process. Additional images can be captured until thecomplete surface has been measured, up to the limit of the mechanicalstage that moves the measured object. The edge of each additional imageshould either touch the previous image or overlap the previous imagevery slightly. The data from the additional image can be stitched to theoriginal image via software.

In a third illustrative embodiment of the present application, theoptical detector is a linear array of detector elements positioned forinstance in the Y direction. The reference mirror moves continuouslyback and forth toward and away from the beam splitter in sinusoidalmotion, or the wavelength of the light source changes in sinusoidalfashion, and the signal processing apparatus determines phaseinformation by analyzing the output of each element of the opticaldetector. The sample moves in the X direction while image data are beingacquired, as shown in FIG. 4a . The pixel size in the Y direction isequal to the physical size of a detector element divided by themagnification of objective lens 220. The pixel size in the X directionin this example is equal to the speed of sample movement in the Xdirection divided by the detection rate. The detection rate is dependenton both the frame rate of the optical detector and the signal processingtechnique used to detect phase changes. The maximum detection rateachievable is the frame rate, with some signal processing techniquesachieving slower rates such as fps/2, fps/4, and fps/64, as aredisclosed herein, where fps is an abbreviation for frames per second.

For example a sample moving at 1400 millimeters per second in the Xdirection and an optical detector sampling at 140,000 frames per secondcan produce a pixel size in the X direction of 10 microns, when using asignal processing technique that can detect phase information using onlyone frame of image data. The Y dimension of the image size created usingthis illustrative embodiment is equal to the physical length of thelinear optical detector reduced by the magnification of objective lens220. The X dimension of the image size created using this illustrativeembodiment is equal to the X distance moved by the sample divided by thedetection rate. To measure a surface of larger area, it is possible toperform a Step and Repeat operation, as previously described, and stitchtogether multiple images.

In this example, the measured surface is divided into many 10 micron by10 micron pixels, so according to the Nyquist sampling theory it ispossible to detect changes in surface topology having a spatialfrequency of 1/(2*10 microns), or 50 cycles per millimeter. Theamplitude of the topology variations that can be detected is dependenton the modulation frequency of the optical path length and the stagescan speed. In the case of using a HeNe laser source of wavelength 632nm, modulating the reference mirror by 316 nm peak to peak, and using acamera sampling at 140,000 frames per second, the system can detect amaximum height difference of 316 nm from one pixel to the next in theY-direction or between frames of the pixel in the X-direction.

The minimum required modulation frequency ω_(r) of the reference beampath length or the light source wavelength depends on the choice ofdemodulation technique, and the present application discloses fourtechniques, as follows,

-   -   1. Active mixing    -   2. Pseudo-active mixing    -   3. Multi-frequency analysis, and    -   4. Multi-frequency analysis via Phase Locked Loop.

When using active mixing, pseudo-active mixing, or multi-frequencyanalysis (without phase locked loop) the minimum required modulationfrequency ω_(r) is a function of the camera frame rate, the requiredsurface profile spatial resolution, the speed of movement of themeasured sample, and the profile accuracy. If the surface structure hasa period of p in the X direction as shown in FIG. 5, the fringe phasethat the jth pixel would see can be expressed as

$\varphi_{j} = {{C\;{\cos\left( {{\frac{2\pi}{p}X} + \theta_{0}} \right)}} + {DX} + {\varphi_{0}.}}$

D is the deviation from absolute perpendicularity between themeasurement beam and the average measured surface, θ₀ is the offset ofthe phase, and φ₀ is the offset of the ω_(r) modulation. In practice,when the measurement sample is aligned such that it is substantiallyperpendicular to the measurement beam, then D can be considered zero.When the beam position moves at a constant speed v, a plot of the phaseoutput versus time is a cosine function. The faster the measured surfacemoves under the measurement beam the higher frequency of the outputintensity signal. The modulation frequency can thus be expressed as

$\omega_{r}\operatorname{>>}{\frac{\mathbb{d}\varphi_{j}}{\mathbb{d}t} = {{{- C}\;\frac{2\pi\; v}{p}{\sin\left( {{\frac{2\pi\; v}{p}t} + \theta_{0}} \right)}} + {{Dv}.}}}$

When signal processing incorporating a phase locked loop, such as theknown method disclosed in U.S. Pat. No. 7,430,484, or any other suitablemethod is used, the minimum modulation frequency of ω_(r) can be 3-4times lower for the same stage movement speed.

In a fourth illustrative embodiment of the present application, theoptical detector is a linear array of optical detector elementspositioned to look at the radial direction of a circular measuredsurface, as shown in FIG. 4b . For example, the linear array of opticaldetector elements and/or the circular measured surface can be configuredto move relative to one another to allow the optical detector to performa measurement along a radius of the measured surface. In accordance withthe illustrative embodiment of FIG. 4b , the reference mirror movescontinuously back and forth in sinusoidal motion, or the wavelength ofthe light source 212 is modulated in sinusoidal fashion, and the signalprocessing apparatus determines phase information by analyzing theoutput of each element of the optical detector. The measured objectrotates about an axis 32 which passes through the center point of themeasured object with the measured surface 36 substantially perpendicularto the measurement beam 230 a. Image data are being acquired while thesurface 36 is rotating. The pixel size in the radial direction is equalto the physical size of an optical detector element divided by themagnification of the objective lens 220. The pixel size in the thetadirection is equal to the angular rotational speed of sample movement,times the radius of the pixel being measured, divided by the detectionrate. While the size of a pixel in the theta direction is not constantdue to the differing radii of each optical detector element, thisdifference can be readjusted later when presenting data. It is possibleto acquire multiple images, in Step and Repeat fashion, by moving thelinear array of optical detectors in the radial direction afteracquiring an image of one complete revolution of the sample. The speedof rotation of the sample can be changed when acquiring different imagesin order to reduce the angular variation in pixel size and reduce thetotal measurement time.

Referring to FIG. 6, the signals from each pixel in the optical detector222 are captured, digitized by a digitizer 29, transferred to a framegrabber 30, and fed to a signal processing component 31, such as a GPU,a Field Programmable Gate Array (FPGA), or any other suitable signalprocessing component. Xilinx Spartan 3A DSP 1800A is an example of asuitable FPGA.

Some optical detectors include the capability to digitize the opticalintensity of each pixel, and other optical detectors produce an analogoutput which must be digitized external to the optical detector.

All of the illustrative embodiments of the present application describedabove can measure distance in units of the average wavelength of lightemitted from the light source 212. Unforeseen short-term changes inwavelength therefore create measurement errors. These errors, andsimilar errors such as might be caused by a change in the refractiveindex of air, can be avoided, as shown in FIG. 7.

FIG. 7 shows an interferometry system 700, in which an additionaloptical detector element 706 a can be positioned adjacent to opticaldetector elements 706 b, 706 c within the optical detector 222previously described. Further, an additional fixed measured surface 702can be positioned adjacent to the measured surface 210, such that thephysical path length of the additional measured surface 702 does notchange when the physical path length to the measured surface 210changes. Changes in the phase of the intensity signal from each pixel ofthe measured surface, once converted to distance, can be multiplied bythe ratio of the original phase of the pixel measuring the fixed surfaceto the current phase of the pixel measuring the fixed surface tocompensate for change in wavelength or refractive index. This correctioncan be made in real time, because all pixel data are sampled at the sametime, and the data are processed in parallel by the signal processor 31.

The optical configuration is shown in FIG. 7. The surface 702 is thefixed surface, and the surface 210 is the measured surface. The beam 230a is large enough to strike both the measured surface 210 and the fixedsurface 702. The beam 230 b is reflected by the partially mirroredsurface 216 and then combined with the portion of reflected beam 224 bthat is transmitted through the partially mirrored surface 216. Thecombination of those beams, namely, the beam 232, enters the lens 220and is expanded to become beams 704 a, 704 b, 704 c. Specifically, thebeam 704 c is the ray of light at one side of a complete beam comprisingbeams 704 a, 704 b, 704 c, the beam 704 b is the ray at the center ofthe complete beam, and the beam 704 a is the ray at the side of thecomplete beam opposite the beam 704 c. The optical detector 222 in thisexample is a linear array of optical detector elements 706 a, 706 b, 706c. The beam 704 c is detected by the optical detector element 706 c, thebeam 704 b is detected by the optical detector element 706 b, and thebeam 704 a is detected by the optical detector element 706 a.

The waveform of the intensity for each pixel can be expressed asI(x,y,t)=A(x,y)+B(x,y)cos(Δφ*sin(ω_(r) t)+φ(x,y,t))where x and y represent the location of the position being measured, Ais a DC signal offset which may vary from one measurement site toanother, ω_(r) is the angular frequency of the modulation of thereference surface position or the wavelength, B is the intensityamplitude of the waveform, φ is the phase of the fringe pattern as aresult of interference, and Δφ is the range of phase shift due to motionof the reference mirror. The DC offset term can be ignored, and theremainder of the equation can be represented by a Fourier series asfollows.

$\begin{matrix}{{I\left( {x,y,t} \right)} = {{{B\left( {x,y} \right)}{\cos\left( {{\Delta\;\varphi*{\sin\left( {\omega_{r}t} \right)}} + {\varphi\left( {x,y,t} \right)}} \right)}} = {{{{BJ}_{0}\left( {\Delta\;\varphi} \right)}{\cos(\varphi)}} - {2\; B\;{\sin(\varphi)}{\Sigma\left\lbrack {{J_{{2m} - 1}\left( {\Delta\;\varphi} \right)}{\sin\left( {\left( {{2m} - 1} \right)*\omega_{r}t} \right)}} \right\rbrack}}}}} & (1) \\{\mspace{20mu}{{+ 2}B\;{\cos(\varphi)}{\Sigma\left\lbrack {{J_{2m}\left( {\Delta\;\varphi} \right)}{\cos\left( {2m\;\omega_{r}t} \right)}} \right\rbrack}}} & (2)\end{matrix}$where the summation is from m=1 to ∞, J_(i)(Δφ) for i=0, 1, 2, . . . areBessel functions, and the DC signal offset term is omitted forsimplicity. An exemplary method of measuring the phase φ of each pixellocation is to calculate the arc tangent [α*SN(φ)/CS(φ)] at thatlocation, where α is a constant dependent only on Δφ. The term SN(φ) isused as a short-hand for the demodulated result using odd harmonics inthe output signals, I(x,y,t), such as −Bsin(φ,x,y,t){J₁(Δφ)+J₃(Δφ)+J₅(Δφ)+ . . . }. The constant gain−B{J₁(Δφ)+J₃(Δφ)+J₅(Δφ)+ . . . } for sin(φ,x,y,t) could vary dependingon the synthesized oscillator configuration. The term CS(φ) is used as ashort-hand for the demodulated result using even harmonics signals, suchas B cos(φ,x,y,t){J₂(Δφ)+J₄(Δφ)+J₆(Δφ)+ . . . }. Again, the constantgain for cos(φ,x,y,t) could vary depending on the synthesized oscillatorconfiguration. Therefore once these terms SN(φ) and CS(φ) are obtainedfor each pixel X,Y position, the distance Z at each pixel can becalculated. With this exemplary method, the noise spectrum outside ofthe fringe oscillation frequency and its harmonics is effectivelyeliminated by a phase synchronous detection technique, while themeasurement range can be well beyond the fringe period.

Similar waveforms produced by position encoders are known. Further,methods of calculating position information from such output signals arealso known, e.g., by using a probe or a sensor that moves in asinusoidal motion parallel to a grating surface and substantiallyperpendicular to the direction of the grating stripes, as disclosed inU.S. Pat. Nos. 5,589,686, 5,744,799, 6,639,686, and 7,430,484, which areincorporated herein by reference in their entirety.

The signal processing shown in FIG. 8a determines phase φ of theintensity signal by calculating sin(φ) and cos(φ) and taking the arctangent. Multiplying the intensity signal I(x,y,t) by cos(2ω_(r)t) andfiltering through a low pass filter creates the coefficient for m=1, ½*Bcos(φ)J₂(Δφ). Similarly, multiplying the intensity signal I(x,y,t) bysin(ω_(r)t) and filtering through a low pass filter creates thecoefficient for m=1, ½*B sin(φ)J₁ (Δφ).φ=arc tangent(J ₁(Δφ)/J ₂(Δφ)*[½*B cos(φ)J ₂(Δφ)]/[½*B sin(φ)J ₁(Δφ)]).

Sin(φ) in the Fourier series of equation 2 has a coefficient of2B*Σ[J_(2m−1)(Δφ)sin((2m−1) *ω_(r)t)], and cos(φ) has a coefficient of2B*Σ[J_(2m)(Δφ)cos(2mω_(r)t)]. The constant shown in FIG. 8a is theratio of the cos(φ) coefficient divided by the sin(φ) coefficient. Thearc tangent function can be computed via a look-up table, a numericalprocessing algorithm, or any other suitable technique.

The output of the arc tangent computation is φ, which can be convertedto a distance by multiplying by

$\frac{\lambda}{4\pi}.$The actual measured distance is φ+nλ, where n is an integer. The processof determining the value of n is referred to as “phase unwrapping”.Phase unwrapping is done by comparing the distance measured at one pixelto neighboring pixels and picking a value of n such that the differencebetween a pixel and its neighbor is less than λ/2.

Multiplying the I(x,y,t) signal by cos(4ω_(r)t) and sin(3ω_(r)t) createsthe coefficients of sin(φ) and cos(φ) for the case of m=2, and addingthe coefficient for m=1 to the coefficient for m=2 before computing thearc tangent creates an improved determination of φ. Computing thecoefficients of sin(φ) and cos(φ) using additional values of m creates abetter determination of φ. FIG. 8b shows how the signal processing woulddetermine φ using m=1 through m=4, inclusive.

Alternatively, a pseudo-phase-locked loop (PLL) can be used to create anestimate of the phase φ, {circumflex over (φ)}, and to computecos({circumflex over (φ)})sin(nω_(r)t), where n is an odd integer, andsin({circumflex over (φ)})cos(mω_(r)t), where m is an even integer, andmultiply-add the incoming intensity signal I(x,y,t) by the synthesizedfunctions with the estimated quadrature components, for example, asdescribed in U.S. Pat. No. 7,430,484. The PLL constantly adjusts theestimate of phase {circumflex over (φ)} so that sin(φ−{circumflex over(φ)}) is zero, and determines the reference mirror oscillation amplitudeΔφ) rather than requiring Δφ as an input, thereby eliminating errorscaused by variation in or an inaccurate value of Δφ, the referencemirror oscillation amplitude.

In the second, third, and fourth illustrative embodiments of the presentapplication described above, the data for all optical detector elementsare processed in substantially real time, in parallel. This may be doneeither via multiple processor cores or preferably by an FPGA (FieldProgrammable Gate Array), a GPU (Graphics Processing Unit), or an ASIC(Application Specific Integrated Circuit) utilizing pipe-lined signalprocessing, in which the same hardware quickly processes an intensitydatum from one optical detector element and then processes an intensitydatum from the next optical detector element by transferring the outputfrom each node to the next processing node at each clock cycle of theprocessor, producing fully processed intensity data at a rate that canbe as fast as the rate that data are captured by the optical detectorwith a delay of only a few clock cycles of the pipe-line.

FIG. 9 shows an exemplary signal processing flow using pipe-lining,although variations are possible. Intensity information I_(j) coming outof the camera, where j refers to the row j of the linear opticaldetector array in the third illustrative embodiment is fed into theprocessor core through the memory array, MA3 at every clock cycle. Eachsine and cosine signal is multiplied by an appropriate gain, which isdetermined from a look-up table. All the cosine terms and all the sineterms are added. When the jth pixel data is multiplied by thesynthesized multi-frequency signals, the result is fed into a low passfilter at the next processor clock cycle in order to derive A*SN(φ) andB*CS(φ), where A and B are constants. While this is happening,processing of the next intensity signal starts at the previousfunctional node. The low pass filters have a few intermediate stateswhich correspond to a pixel position. Such states are stored inFIFO-like memory MA1, and are later restored immediately before the nextcorresponding pixel operation is executed. The intermediate result fromthe lower signal path is then multiplied by the constant depending onthe gain matrix inside Gain LUT. The last signal processing core firstcalculates arc tangent(S/C). The arc tangent function creates an outputφ, whereas what is needed is φ+nπ where n is an integer, such that thedifference in phase between the current pixel and the same pixel in thenext frame is less than π, in order to guaranty continuity. This processof phase unwrapping is the last step in the signal process flow shown inFIG. 9. Each phase measurement result is stored in memory array MA2 andis later compared with the arc tangent output at the same pixel positionat the next frame. If the difference is more than π, the latest phasemeasurement result is readjusted by ±π depending on the surface profileuntil the absolute phase difference becomes less than π.

Alternatively, the PLL signal processing method disclosed in U.S. Pat.No. 7,430,484 can be used for pipe-lined processing. Use of thistechnique creates automatic phase unwrapping, as the input to thenumerical integrator in the feedback loop constantly shows the phasebeing measured and automatically maintains continuity as the measuredphase changes.

Pipe-lining makes it economically feasible to process all data from theoptical detector elements in real time, even when there are millions ofpixels in the image. Further, the processing techniques described in theabove listed U.S. patents allow resolution of phase measurementequivalent to one part in 2^18. Thus the Z-axis resolution of themeasurement when using a Michelson interferometer and light of 632 nmwavelength is 1.2 pm.

The signal processing method described thus far is referred to as a“multi-frequency” analysis method. This method requires a good digitalrepresentation of the input signal I(x,y,t). Typically 64 or moresamples per period of path length modulation frequency ω_(r) arerequired, especially when analyzing higher order harmonics. Providing 64samples via an optical detector array such as a CCD camera requires 64frames of data. In the second, third, and fourth illustrativeembodiments described above, the measured object is moving during dataacquisition and therefore the effective pixel dimension in the directionof movement equals the distance traveled divided by the effective framerate, which has been referred to as the “detection rate”.

Making the detection rate 1/64 the camera frame rate limits the totalmeasurement speed. This problem can be addressed by avoiding the initialmultiplication of the digitized intensity waveform shown in FIGS. 8a and8b . Employing a light intensity modulator 1202 (see FIG. 12) tomodulate the physical light intensity of the light source 212 (see alsoFIG. 12) by sin(ω_(r)t), with the light modulation frequency, ω_(r),synchronous with the camera frame rate, produces a signal with the sameinformation as multiplying the intensity signal I(x,y,t) produced usinga light source of constant intensity by sin(ω_(r)t). Similarly,employing the light intensity modulator 1202 to modulate the physicallight intensity of the light source 212 by cos(2ω_(r)t) produces asignal with the same information as multiplying the intensity signalI(x,y,t) produced using a light source of constant intensity bycos(2ω_(r)t).

When multiplication is done digitally it is possible to multiply theintensity signal I(x,y,t) by sin(ω_(r)t) and also by cos(2ω_(r)t) andproduce two outputs at the same time. When modulating the physical lightintensity rather than the intensity signal I(x,y,t), the physical lightintensity can only be modulated by a single waveform. Since it isnecessary to obtain both sin(φ) and cos(φ) information one can modulatethe physical light intensity by sin(ω_(r)t) for one cycle, modulate thephysical light intensity by cos(2ω_(r)t) for the next cycle, repeat thesequence, combine information obtained from different cycles to obtainthe sin(φ) and cos(φ), and compute the arc tangent[sin(φ)/cos(φ)] (seeFIG. 12, reference numeral 1208). Since the sine and cosine functionsinclude both positive and negative values, the intensity signal isactually modulated by [1+sin(ω_(r)t)] and [1+cos(2ω_(r)t)], and the DClevel is removed during signal processing. FIG. 10 shows one example ofwaveforms produced when modulating the physical light intensity in thismanner.

Define +S as the photon signal arriving at the optical detector 222 (seeFIG. 12) during one cycle of path length modulation of frequency φ_(r)when the physical light intensity is modulated by sin(φ_(r)t). Define +Cas the photon signal arriving at the optical detector 222 during onecycle of path length modulation of frequency φ_(r) when the physicallight intensity is modulated by cos(2φ_(r)t), which in this example isduring the second modulation cycle. During the third cycle, −S isobtained when the physical light intensity is modulated by −sin(φ_(r)t).During the fourth cycle, −C is obtained when the physical lightintensity is modulated by −cos(2φ_(r)t). The sequence then repeats, withthe fifth cycle being the same as the first, the sixth cycle being thesame as the second, etc.

Define d as the DC offset of the pixel intensity signal caused by thefact that the physical light intensity was modulated by [1+sin(φ_(r)t)]rather than by [sin(φ_(r)t)] and [1+cos(2φ_(r)t)] rather than[cos(2φ_(r)t)]. The optical detector 222 (such as a CCD camera)integrates the incoming photons within a finite time window per frame.This integration performs a function equivalent to the low pass filterof FIG. 8a or 8 b. As a result, the integration operation of the opticaldetector 222 (see FIG. 12) denoted as <> below, provides the outputsignals of a1, a2, a3, and a4 shown in FIG. 10 during each frame asfollows (see also FIG. 12, reference numeral 1204).a1=<+S+d>  (3)a2=<+C+d>  (4)a3=<−S+d>  (5)a4=<−C+d>  (6)

Although it requires four periods of reference mirror modulation offrequency φ_(r) to acquire +S, −S, +C, and −C values, after acquiringdata for four frames, a new estimate of S, indicated by the letter Swith the mark ^ over it, can be computed after each successive oddnumbered frame, and a new estimate of C, indicated by the letter C withthe mark ^ over it, can be computed after each successive even numberedframe (see FIG. 12, reference numeral 1206).Ŝ=(a1−a3)/2,  (7)Ĉ=(a2−a4)/2,  (8){circumflex over (d)}=(a1+a3)/2 or {circumflex over (d)}=(a2+a4)/2  (9)

Although the modulation of the physical light intensity when doingactive mixing is synchronous with the motion of the reference mirror,the discontinuity in the intensity signal that may be produced whenswitching instantaneously from sin(φ_(r)t) to cos(2φ_(r)t) modulationmay create an error in the CCD image. Further, a CCD or CMOS camera maynot integrate photons over 100% of the period of the frame rate, causingan additional error source. In order to avoid these error sources, onecan modulate the path length multiple cycles per frame and leave onecycle out, which overlaps with the camera non-integration zone, fromphoton integration by keeping the modulated physical light intensityzero during the cycle. This lowers the sensitivity of the camerasomewhat in order to avoid these error sources.

The physical light intensity of the light source 212 (see FIG. 12), suchas a constant intensity laser light source, can be modulated via thelight intensity modulator 1202 (see also FIG. 12), such as anacousto-optic modulator or any other suitable mechanism or technique, asknown in the art. Such an intensity modulator generally adds cost to theinterferometer, but the increased speed of measurement may justify theadded cost as this signal processing technique achieves an effectiveframe rate of fps or fps/2 rather than for instance fps/64.

Another technique, referred to as “pseudo-active mixing”, can acquiredata at an effective maximum rate of fps/4 and does not requiremodulating the intensity of the light source. FIG. 11 shows signals inthe pseudo-active mixing process. Here, the frame capture timing and thepath length modulation timing is aligned such that the integral of thepath length modulation signal over time period 1 is zero. Sin(φ) isobtained by multiplying the intensity signal by modulation signal 1, andcos(φ) is obtained by multiplying the intensity signal by modulationsignal 2. There is no real multiplication because modulation signals 1and 2 take on values of only +1, −1, and 0. Thus the processing hardwarerequired is considerably simpler. The result of multiplying theintensity signal by modulation signal 1 consists of the camera intensityoutput created at the end of time segment 2 minus the camera intensityoutput created at the end of time segment 4. The result of multiplyingthe camera intensity signal by modulation signal 2 consists of alphatimes the quantity [the camera intensity output created at the end oftime segment 1 minus the camera intensity output created at the end oftime segment 2 plus the camera intensity output created at the end oftime segment 3 minus the camera intensity output created at the end oftime segment 4], where alpha is a constant. After 4 frames of camerainformation it is possible to calculate the phase. After time segment 5it is desirable to re-calculate phase using the camera outputs from timesegments 2-5. The process is repeated in pipe-lined fashion producing anew phase estimate after each camera frame, with the estimate based onthe four most recent camera frames.

It will be appreciated by those skilled in the art that modifications toand variations of the above-described systems and methods may be madewithout departing from the inventive concepts disclosed herein.Accordingly, the disclosure should not be viewed as limited except as bythe scope and spirit of the appended claims.

What is claimed is:
 1. An interferometer, comprising: a beam splitteroperative to split a source light beam into a reference beam and ameasurement beam, the reference beam for striking a reference surface,and the measurement beam for striking a measurement sample;one-dimensional array of optical detector elements operative to receivea combination of light beams reflected from the reference surface andthe measurement sample, respectively, and to detect interference fringesresulting from the combination of light beams, the one-dimensional arrayof optical detector elements being operative to detect an intensitysignal, l(x,y,t), corresponding to an intensity of at least a portion ofthe combination of light beams at a pixel position, x,y, and at a time,t; a modulator operative to modulate a wavelength of the source lightbeam at a predetermined sinusoidal frequency, ω_(r); and signalprocessing means including at least arctangent logic means and phaseunwrapping logic means, the signal processing means being operative: tocompute, by the arctangent logic means, an arctangent of a quotient of afirst signal, αI(x,y,t)sin(ω_(r)t), divided by a second signal,I(x,y,t)cos(2ω_(r)t), wherein “α” is a predetermined constant, andwherein the computed arctangent corresponds to one or more phases of theinterference fringes; and to unwrap, by the phase unwrapping logicmeans, the one or more phases of the interference fringes to obtain oneor more physical distances relative to the measurement sample.
 2. Theinterferometer of claim 1 wherein the one-dimensional array of opticaldetector elements is configured to be positioned substantiallyperpendicular to a direction of linear movement of the measurementsample, and to perform a measurement on the measurement sample bycollecting intensity data while the measurement sample moves in thepredetermined linear direction of movement.
 3. The interferometer ofclaim 1 wherein the measurement sample is substantially circular, andwherein the one-dimensional array of optical detector elements isconfigured to perform a measurement on the measurement sample bycollecting intensity data along a radius of the measurement sampleduring rotational movement of the measurement sample.
 4. Aninterferometer, comprising: a light intensity modulator operative: tomodulate a light intensity of a source light beam by sin(i*ω_(r)t) for kperiods of a predetermined sinusoidal frequency, ω_(r), to obtain afirst modulated signal; and to modulate the light intensity of thesource light beam by cos(j*ω_(r)t) for k periods of the predeterminedsinusoidal frequency, ω_(r), to obtain a second modulated signal,wherein “i” is an odd integer, wherein “j” is an even integer, andwherein “k” is a positive integer; a beam splitter operative to splitthe intensity modulated source light beam into a reference beam forstriking a reference surface, and a measurement beam for striking ameasurement sample, wherein a light beam reflected from the referencesurface has an optical path length that is measurable in wavelengths ofthe reference beam; an optical detector operative to receive acombination of light beams reflected from the reference surface and themeasurement sample, respectively, and to detect interference fringesresulting from the combination of light beams, the optical detectorhaving at least one optical detecting element operative to detect anintensity signal, I(x,y,t), corresponding to an intensity of at least aportion of the combination of light beams at a pixel position, x,y, andat a time, t, wherein the first modulated signal is expressed asαI(x,y,t)sin(ω_(r)t), wherein the second modulated signal is expressedas I(x,y,t)cos(2ω_(r)t) and wherein “α” is a predetermined constant; alight wavelength modulator operative to modulate the optical path lengthof the light beam reflected from the reference surface at thepredetermined sinusoidal frequency, ω_(r), by modulating a wavelength ofthe source light beam at the predetermined sinusoidal frequency, ω_(r);and signal processing means including at least arctangent logic meansand phase unwrapping logic means, wherein the arctangent logic means isoperative to compute an arctangent of a quotient of the first modulatedsignal divided by the second modulated signal, the computed arctangentcorresponding to one or more phases of the interference fringes, andwherein the phase unwrapping logic means is operative to unwrap the oneor more phases of the interference fringes to obtain one or morephysical distances relative to the measurement sample.
 5. Theinterferometer of claim 4 wherein the light intensity modulator is anacousto-optic modulator.
 6. An interferometer, comprising: a beamsplitter operative to split a source light beam into a reference beamfor striking a reference surface, and a measurement beam for striking ameasurement sample, wherein the reference beam has an optical pathlength that is measurable in wavelengths of the reference beam; anoptical detector operative to receive a combination of light beamsreflected from the reference surface and the measurement sample,respectively, and to detect interference fringes resulting from thecombination of light beams, wherein the optical detector has at leastone optical detecting element operative to detect an intensity signal,I(x,y,t), corresponding to an intensity of at least a portion of thecombination of light beams at a pixel position, x,y, and at a time, t,wherein the optical detector has an associated frame rate, and wherein“φ” represents one or more phases of the interference fringes; amodulator operative to modulate a wavelength of the source light beam ata predetermined sinusoidal frequency, (ω_(r), that is synchronous withthe frame rate of the optical detector, thereby modulating the opticalpath length measurable in wavelengths of the reference beam; and signalprocessing means operative: to calculate a sine of φ by applying a firstpredetermined modulation signal to the intensity signal, I(x,y,t), thefirst predetermined modulation signal being periodic and having valuesof 0, 1, 0, and −1 during four consecutive time segments, each of thefour consecutive time segments corresponding to a modulation period ofthe optical path length of the reference beam; to calculate a cosine ofφ by applying a second predetermined modulation signal to the intensitysignal, I(x,y,t), the second predetermined modulation signal beingperiodic and having values of 1, −1, 1, and −1 during the fourconsecutive time segments; to obtain the one or more phases, φ of theinterference fringes from the sine of φ and the cosine of φ; and tounwrap the one or more phases, φ, of the interference fringes to obtainone or more physical distances relative to the measurement sample.
 7. Amethod of operating an interferometer, comprising: splitting, by a beamsplitter, a source light beam into a reference beam and a measurementbeam, the reference beam for striking a reference surface, and themeasurement beam for striking a measurement sample; receiving, at aone-dimensional array of optical detector elements, a combination oflight beams reflected from the reference surface and the measurementsample, respectively; detecting, by the one-dimensional array of opticaldetector elements, interference fringes resulting from the combinationof light beams, the detecting of the interference fringes includingdetecting, by the one-dimensional array of optical detector elements, anintensity signal, I(x,y,t), corresponding to an intensity of at least aportion of the combination of light beams at a pixel position, x,y, andat a time, t, wherein a light beam reflected from the reference surfacehas an optical path length that is measurable in wavelengths of thereference beam; modulating, by a modulator, a wavelength of the sourcelight beam at a predetermined sinusoidal frequency, ω_(r), therebymodulating the optical path length of the light beam reflected from thereference surface at the predetermined sinusoidal frequency, ω_(r);computing, by arctangent logic means, an arctangent of a quotient of afirst signal, αI(x,y,t)sin(ω_(r)t), divided by a second signal,I(x,y,t)cos(2ω_(r)t) “α” being a predetermined constant, the computedarctangent corresponding to one or more phases of the interferencefringes; and unwrapping, by phase unwrapping logic means, the one ormore phases of the interference fringes to obtain one or more physicaldistances relative to the measurement sample.
 8. The method of claim 7further comprising: moving the measurement sample in a predeterminedlinear direction of movement; positioning the one-dimensional array ofoptical detector elements substantially perpendicular to thepredetermined linear direction of movement of the measurement sample;and performing, by the one-dimensional array of optical detectorelements, a measurement on the measurement sample by collectingintensity data while moving the measurement sample in the predeterminedlinear direction of movement.
 9. The method of claim 7 wherein themeasurement sample is substantially circular, wherein the measurementsample has a radius, and wherein the method further comprises:rotationally moving the measurement sample; and performing, by theone-dimensional array of optical detector elements, a measurement on themeasurement sample by collecting intensity data along the radius whilerotationally moving the measurement sample.
 10. A method of operating aninterferometer, comprising: modulating a physical light intensity of asource light beam by sin(i*ω_(r)t) for k periods of a predeterminedsinusoidal frequency, ω_(r), to obtain a first modulated signal, “i”being an odd integer, “j” being an even integer, and “k” being apositive integer; modulating the physical light intensity of the sourcelight beam by cos(j*ω_(r)t) for k periods of the predeterminedsinusoidal frequency, ω_(r), to obtain a second modulated signal;splitting, by a beam splitter, the intensity modulated source light beaminto a reference beam and a measurement beam, the reference beam forstriking a reference surface, and the measurement beam for striking ameasurement sample, a light beam reflected from the reference surfacehaving an optical path length that is measurable in wavelengths of thereference beam; receiving, at an optical detector, a combination oflight beams reflected from the reference surface and the measurementsample, respectively; detecting, by the optical detector, interferencefringes resulting from the combination of light beams, includingdetecting, by at least one optical detecting element, an intensitysignal, I(x,y,t), corresponding to an intensity of at least a portion ofthe combination of light beams at a pixel position, x,y, and at a time,t, the first modulated signal being expressed as αI(x,y,t)sin(ω_(r)t),the second modulated signal being expressed as I(x,y,t)cos(2ω_(r)t), and“α” being a predetermined constant; modulating, at the predeterminedsinusoidal frequency, ω_(r), the optical path length of the light beamreflected from the reference surface; computing, by arctangent logicmeans, an arctangent of a quotient of the first modulated signal dividedby the second modulated signal, the computed arctangent corresponding toone or more phases of the interference fringes; and unwrapping, by phaseunwrapping logic means, the one or more phases of the interferencefringes to obtain one or more physical distances relative to themeasurement sample.
 11. The method of claim 10 wherein the source lightbeam has an optical path, wherein the method further comprises: placingan acousto-optic modulator in the optical path of the source light beam,wherein the modulating of the physical light intensity of the sourcelight beam by sin(i*ω_(r)t) for k periods of the predeterminedsinusoidal frequency, ω_(r), includes modulating the physical lightintensity of the source light beam using the acousto-optic modulator;and wherein the modulating of the physical light intensity of the sourcelight beam by cos(j*ω_(r)t) for k periods of the predeterminedsinusoidal frequency, ω_(r), includes modulating the physical lightintensity of the source light beam using the acousto-optic modulator.12. A method of operating an interferometer, comprising: splitting, by abeam splitter, a source light beam into a reference beam for striking areference surface, and a measurement beam for striking a measurementsample, the reference beam having an optical path length that ismeasurable in wavelengths of the reference beam; receiving, at anoptical detector, a combination of light beams reflected from thereference surface and the measurement sample, respectively; detecting,by the optical detector, interference fringes resulting from thecombination of light beams, including detecting, by at least one opticaldetecting element, an intensity signal, I(x,y,t), corresponding to anintensity of at least a portion of the combination of light beams at apixel position, x,y, and at a time, t, the optical detector having anassociated frame rate, and “φ” representing one or more phases of theinterference fringes; modulating the optical path length of the lightbeam reflected from the reference surface at a predetermined sinusoidalfrequency, ω_(r), that is synchronous with the frame rate of the opticaldetector; calculating, by signal processing means, a sine of φ byapplying a first predetermined modulation signal to the intensitysignal, I(x,y,t), the first predetermined modulation signal beingperiodic and having values of 0, 1, 0, and −1 during four consecutivetime segments, the four consecutive time segments each corresponding toa modulation period of the optical path length of the reference beam;calculating, by the signal processing means, a cosine of φ by applying asecond predetermined modulation signal to the intensity signal,I(x,y,t), the second predetermined modulation signal being periodic andhaving values of 1, −1, 1, and −1 during the four consecutive timesegments; obtaining, by the signal processing means, the one or morephases, φ, of the interference fringes from the sine of φ and the cosineof φ; and unwrapping, by the signal processing means, the one or morephases, ω, of the interference fringes to obtain one or more physicaldistances relative to the measurement sample.
 13. A method of operatingan interferometer, comprising: splitting, by a beam splitter, a sourcelight beam into a reference beam and a measurement beam, each of thereference beam and the measurement beam having an optical path and anoptical path length; transmitting the measurement beam through ameasurement sample in the optical path of the measurement beam;receiving, at a one-dimensional array of optical detector elements, acombination of the reference beam and the measurement beam transmittedthrough the measurement sample; detecting, by the one-dimensional arrayof optical detector elements, interference fringes resulting from thecombination of beams, the detecting of the interference fringesincluding detecting an intensity signal, I(x,y,t), corresponding to anintensity of at least a portion of the combination of beams at a pixelposition, x,y, and at a time, t; modulating, by a modulator, awavelength of the source light beam at a predetermined sinusoidalfrequency, ω_(r); computing, by arctangent logic means, an arctangent ofa quotient of a first signal, αI(x,y,t)sin(ω_(r)t), divided by a secondsignal, I(x,y,t)cos(2ω_(r)t) “α” being a predetermined constant, thecomputed arctangent corresponding to one or more phases of theinterference fringes, and unwrapping, by phase unwrapping logic means,the one or more phases of the interference fringes to obtain one or morephysical distances relative to the measurement sample.
 14. The method ofclaim 13 further comprising: moving the measurement sample in apredetermined linear direction of movement; positioning theone-dimensional array of optical detector elements substantiallyperpendicular to the predetermined linear direction of movement of themeasurement sample; and performing, by the one-dimensional array ofoptical detector elements, a measurement on the measurement sample whilemoving the measurement sample in the predetermined linear direction ofmovement.
 15. The method of claim 13 wherein the measurement sample issubstantially circular, wherein the measurement sample has a radius, andwherein the method further comprises: rotationally moving themeasurement sample; and performing, by the one-dimensional array ofoptical detector elements, a measurement on the measurement sample alongthe radius while rotationally moving the measurement sample.
 16. Amethod of operating an interferometer, comprising: modulating, by alight intensity modulator, a light intensity of a source light beam bysin(i*ω_(r)t) for k periods of a predetermined sinusoidal frequency,ω_(r), to obtain a first modulated signal, “i” being an odd integer, “j”being an even integer, and “k” being a positive integer; modulating, bythe light intensity modulator, the light intensity of the source lightbeam by cos(j*ω_(r)t) for k periods of the predetermined sinusoidalfrequency, ω_(r), to obtain a second modulated signal; splitting, by abeam splitter, a source light beam into a reference beam and ameasurement beam, each of the source light beam, the reference beam, andthe measurement beam having an optical path and an optical path length,the optical path length of the reference beam being measurable inwavelengths of the reference beam; transmitting the measurement beamthrough a measurement sample in the optical path of the measurementbeam; receiving, at an optical detector, a combination of the referencebeam and the measurement beam transmitted through the measurementsample; detecting, by the optical detector, interference fringesresulting from the combination of the reference beam and the measurementbeam, the detecting of the interference fringes including detecting anintensity signal, I(x,y,t), corresponding to an intensity of at least aportion of the combination of the reference beam and the measurementbeam at a pixel position, x,y, and at a time, t, the first modulatedsignal being expressible as αI(x,y,t)sin(ω_(r)t), the second modulatedsignal being expressible as I(x,y,t)cos(2ω_(r)t), and “α” being apredetermined constant; modulating, by a light wavelength modulator, theoptical path length of the reference beam by modulating a wavelength ofthe source light beam at a predetermined sinusoidal frequency, ω_(r);computing, by arctangent logic means, an arctangent of a quotient of thefirst modulated signal divided by the second modulated signal, thecomputed arctangent corresponding to one or more phases of theinterference fringes; and unwrapping, by phase unwrapping logic means,the one or more phases of the interference fringes to obtain one or morephysical distances relative to the measurement sample.
 17. The method ofclaim 16 wherein the light intensity modulator is an acousto-opticmodulator, wherein the method further comprises: placing theacousto-optic modulator in the optical path of the source light beam,wherein the modulating of the light intensity of the source light beamby sin(i*ω_(r)t) for k periods of the predetermined sinusoidalfrequency, ω_(r), includes modulating the light intensity of the sourcelight beam using the acousto-optic modulator; and wherein the modulatingof the light intensity of the source light beam by cos(j*ω_(r)t) for kperiods of the predetermined sinusoidal frequency, ω_(r), includesmodulating the light intensity of the source light beam using theacousto-optic modulator.
 18. A method of operating an interferometer,comprising: splitting, by a beam splitter, a source light beam into areference beam and a measurement beam, each of the reference beam andthe measurement beam having an optical path and an optical path length,the optical path length of the reference beam being measurable inwavelengths of the reference beam; transmitting the measurement beamthrough a measurement sample in the optical path of the measurementbeam; receiving, at an optical detector, a combination of the referencebeam and the measurement beam transmitted through the measurementsample; detecting, by the optical detector, interference fringesresulting from the combination of the reference beam and the measurementbeam, the detecting of the interference fringes including detecting anintensity signal, I(x,y,t), corresponding to an intensity of at least aportion of the combination of the reference beam and the measurementbeam at a pixel position, x,y, and at a time, t, the optical detectorhaving an associated frame rate, and “φ” representing one or more phasesof the interference fringes; modulating, by a modulator, a wavelength ofthe source light beam at a predetermined sinusoidal frequency, ω_(r),that is synchronous with the frame rate of the optical detector, therebymodulating the optical path length of the reference beam; calculating,by signal processing means, a sine of φ by applying a firstpredetermined modulation signal to the intensity signal, I(x,y,t), thefirst predetermined modulation signal being periodic and having valuesof 0, 1, 0, and −1 during four consecutive time segments, the fourconsecutive time segments each corresponding to a modulation period ofthe optical path length of the reference beam; calculating, by thesignal processing means, a cosine of φ by applying a secondpredetermined modulation signal to the intensity signal, I(x,y,t), thesecond predetermined modulation signal being periodic and having valuesof 1, −1, 1, and −1 during the four consecutive time segments;obtaining, by the signal processing means, the one or more phases, φ, ofthe interference fringes from the sine of φ and the cosine of φ; andunwrapping, by the signal processing means, the one or more phases, φ,of the interference fringes to obtain one or more physical distancesrelative to the measurement sample.